[Getdp] [GetDP] Calculation of an Integral quantity

[Olivier Castany]

> thank you kindly for your reply. I took some time this morning to  
> review your "Torus3D" example, trying to see if I could figure out  
> what X vs. XS is. I noticed a couple of things that are not clear to me:

Hello,

first, a warning : the file torus3D.pro calculates two different 
and independent things :

1) FEM Galerkin method exactly the same as in torus.pro (did 
you look at it ?)

2) Integral quantites

I could have tried to make only the 2nd calculation, but after reading 
Bernhard Kubicek's comments in Tower3DBiot, I thought it would produce 
error messages if there were no "Equation" term, so I wrote 1) and 2) 
in the same file. I have no time now to try and see if it is possible to 
calculate only part 2).

(a warning about Tower3DBiot : I think Bernhard made a mistake and 
should use ZS instead of Z ; in his example, however, this does not make 
a huge difference ; I've mailed him)

> 1) In FunctionSpace, you define function spaces on "D_tot" and  
> "CoilSection", in Formulation, you define an Equation in these, but  
> you also use that FunctionSpace 
               ^^^^
No : there are 3 function spaces : potentiel_vecteur_jauge, 
potentiel_vecteur, champ_mag       

> to define two Quantities that work on "Coil", namely "a2" and "B2". 
                                ^^^^
I don't understand that word in this context.

> How can a Quantity be defined on a  
> region ("Coil") when it has no function space there?

"a2" belongs to the function space "potentiel_vecteur" => a2 lives on 
D_tot (with other words : a2 is defined on D_tot)

The term "In Coil" is the integration domain of the source point :

a2( (X,Y,Z) \in D_tot ) = \int_{(XS,YS,ZS) \ in Coil} mu0 *  
Laplace[]{3D} * J_s_source[] 

(Laplace[]{3D} is a function of (X,XS,Y,YS,Z,ZS) and J_s_source[] is a 
function of (XS,YS,ZS,NormalSource))

> 2) I did note your use of X vs XS, but I still do not understand. To  
> begin with, you seem to use J_s only, defined on X, and not  
> J_s_source, defined on XS. So what is the point of working with XS?  

I do use "J_s_source" ! See the definition of the integral quantities.
Example :

      { Name a2 ; Type Integral ; NameOfSpace potentiel_vecteur ;
        [ mu0 *  Laplace[]{3D} * J_s_source[] ];
        In Coil ; Jacobian JSur ; Integration I ; }

> Does XS only become meaningful if I use certain functions?

I think it is only meaningful in an integral quantity expression.
  
> Can I define where I want my XS to be? If so, how?

See my explaination of the term "In Coil" above.

> 3) The expression "Q(X,...) = \int_{XS,...} q(X,XS,...)" you mention  
> below is pretty much what I am after, but I did not see where or how  
> you implemented this in "Torus3D"?

In the definition of the integral quantities. See above.

Regards,

O.C.